The Hessian Form of an Elliptic Curve

  • N. P. Smart
Conference paper

DOI: 10.1007/3-540-44709-1_11

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2162)
Cite this paper as:
Smart N.P. (2001) The Hessian Form of an Elliptic Curve. In: Koç Ç.K., Naccache D., Paar C. (eds) Cryptographic Hardware and Embedded Systems — CHES 2001. CHES 2001. Lecture Notes in Computer Science, vol 2162. Springer, Berlin, Heidelberg


In this paper we use the Hessian form of an elliptic curve and show that it offers some performance advantages over the standard representation. In particular when a processor allows the evaluation of a number of field multiplications in parallel (either via separate ALU’s, a SIMD type operation or a pipelined multiplication unit) one can obtain a performance advantage of around forty percent.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • N. P. Smart
    • 1
  1. 1.Dept. Computer ScienceUniversity of BristolBristol

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